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A025436 Number of partitions of n into 3 distinct squares.

%I A025436 #15 Nov 11 2015 05:39:17
%S A025436 0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0,1,2,0,0,2,1,0,0,0,
%T A025436 1,1,0,1,1,0,1,2,1,0,0,2,1,0,0,1,2,0,1,2,1,0,1,0,1,1,0,2,2,0,0,3,1,0,
%U A025436 1,2,1,0,0,1,3,1,0,2,1,0,1,1,1,1,1,2,2,0,0,3,3,1,0,1,2,0,0,1,2,0,1,4,0,0,2,2,2,1
%N A025436 Number of partitions of n into 3 distinct squares.
%H A025436 Robert Israel, <a href="/A025436/b025436.txt">Table of n, a(n) for n = 0..10000</a>
%F A025436 G.f.: (1+theta_3(x))^3/48 - (1+theta_3(x))*(1+theta_3(x^2))/8 + (1 + theta_3(x^3))/6, where theta_3 is a Jacobi theta function. - _Robert Israel_, Nov 11 2015
%p A025436 N:= 1000; # to get a(0) to a(N)
%p A025436 A:= Vector(N+1);
%p A025436 for a from 2 to floor(sqrt(N)) do
%p A025436    for b from 1 to min(a-1,floor(sqrt(N-a^2))) do
%p A025436       for c from 0 to min(b-1, floor(sqrt(N-a^2-b^2))) do
%p A025436          x:= a^2 + b^2 + c^2;
%p A025436          A[x+1]:= A[x+1]+1
%p A025436 od od od:
%p A025436 convert(A,list); # _Robert Israel_, Nov 11 2015
%t A025436 n = 100; Clear[A]; A[_] = 0; For[a = 2, a <= Floor[Sqrt[n]], a++, For[b = 1, b <= Min[a-1, Floor[Sqrt[n-a^2]]], b++, For[c = 0, c <= Min[b-1, Floor[Sqrt[n-a^2-b^2]]], c++, x = a^2 + b^2 + c^2; A[x+1] = A[x+1]+1]]]; Array[A, n] (* _Jean-François Alcover_, Nov 11 2015, adapted from _Robert Israel_'s Maple script *)
%K A025436 nonn
%O A025436 0,27
%A A025436 _David W. Wilson_